How was the derivative for the (circled function) found? Only part i don't understand was it the quotient rule?

Question

amistre64 · Answer

quotient rule is overrated since a quotient is just another type of prduct

amistre64 · Answer

$$\frac fg=fg^{-1}$$

amistre64 · Answer

... also, we have no idea what the (circled function) is to start with :/

anonymous · Answer

attachment

anonymous · Answer

my bad forgot to post it

amistre64 · Answer

thats an awful thing to post ...

amistre64 · Answer

f(g)  to  f'(g) * g'

amistre64 · Answer

$$f=4u(u^2+3)^{-1}$$
$$f'=4(u^2+3)^{-1}-4u(2u)(u^2+3)^{-2}$$
$$g=4x^2+7x+1$$
$$g'=8x+7$$

amistre64 · Answer

g(0)=1 so define f'(1) and g'(0)

amistre64 · Answer

and yes, they used the "qoutient rule" on your circled part ...

amistre64 · Answer

if you want to use it; i like to define it in terms of t and b, for top and bottom$$\frac tb\to\frac{bt'-b't}{b^2}$$

anonymous · Answer

i see, lol i understand the quotient rule its just when i tried it i seemd to not get the answer they came out with

anonymous · Answer

never minddd!  lol i found out